Voronoi Diagrams

The Voronoi diagram of a collection of geometric objects is a
partition of space into cells, each of which consists of the points
closer to one particular object than to any others.
These diagrams, their boundaries (medial axes) and their duals (Delaunay triangulations) have
been reinvented, given different names, generalized, studied, and
applied many times over in
many different fields. Voronoi diagrams tend to be involved
in situations where a space should be partitioned into "spheres of influence",
including models of crystal and cell growth as well as protein molecule
volume analysis.

Der
Technik hinter dem Mühlentag (in German).
Kasper Schiess uses Voronoi diagrams to set up web page image maps
of geographical locations
in such a way that clicking on any point in the map leads to a description
of the nearest location.

Image tilings.
The PRISME group at INRIA proposes stitching together multiple images of
a scene (e.g. multiple aerial or satellite views of a piece of land)
using a form of Voronoi diagram to choose which image has the best quality
for each piece of scenery.

Mosaic / stained glass graphic effect. One gets interesting
visual effects by taking a random sample of pixels from a bitmap image,
computing the Voronoi diagram of the sample, and filling each cell
with the corresponding sample's color. This appears to be what
Photoshop does in its "Pixelate->Crystalize" filter;
it can be thought of as a form of piecewise constant function interpolation.

Prove protein volume evaluation software. This project at the
Free University of Brussels
uses Voronoi diagrams and weighted Voronoi diagrams to
analyze the portion of a molecule's volume taken up
by each atom in the molecule.
Mark Gerstein at Stanford has a directory with
very similar software and related papers.

Settlement
selection for interactive display. How to choose which towns to show
on a map, when the scale is too low to show everything?
M. van Kreveld, R. van Oostrum, and J. Snoeyink describe algorithms
based on incremental maintenance of Voronoi diagrams.

Sity.
Tom Kelly appears to be creating artificial cityscapes by using Voronoi diagrams of sites with lots of collinearity to form the city blocks and streets, similar Voronoi diagrams within the blocks to form property boundaries and building floorplans, and straight skeletons for the rooflines.

Skeleton and
boundary extraction. Glynn Robinson of Yale overlays the Delaunay
triangulation and Voronoi diagram of points sampled from a surface
(the boundary between different features in a medical image) and
somehow extracts from them subsets representing the surface itself and
its medial axis.

Voronoi Art.
Scott Sona Snibbe uses a retro-reflective floor to display the Voronoi
diagram of people walking on it, exploring notions of personal space and
individual-group relations.
Additional Voronoi-based art is included in his
dynamic
systems series.